Machin-like formulae
M000412
$$\pi=\frac{48}{5}\arctan\left(\frac{1}{3}\right)+\frac{16}{5}\arctan\left(\frac{1}{57}\right)\frac{-4}{5}\arctan\left(\frac{1}{239}\right)$$
Compact formula
48/5[3] + 16/5[57] - 4/5[239]
Lehmer's measure
3.08587
References
STØRMER (1896)
(full reference coming soon)